This paper discusses the measurement of taxonomic diversity of a given community or set of species. First, given D, the matrix of pairwise distances between species, I propose to summarize taxonomic diversity through Rényi’s information-theoretical parametric formalism on D. In this way, a family of taxonomic diversity indices is obtained which shows different sensitivity to the presence of species with different levels of taxonomic distinctness. The adequacy of information-theoretical indices for quantifying taxonomic diversity is discussed.
Basak, S.C, A.T. Balaban, G.D. Grunwald and B.D. Gute. 2000. Topological indices: Their nature and mutual relatedness. J. Chem. Inf. Comput. Sci. 40: 891–898.
Beck, C. and F. Schlögl. 1993. Thermodynamics of Chaotic Systems. Cambridge University Press, Cambridge.
Berger, W.H. and F.L. Parker. 1970. Diversity of planctonic Foraminifera in deep sea sediments. Science 168: 1345–1347.
Bonchev, D. 1993. Information-Theoretic Indices for Characterization of Chemical Structure. Research Studies Press, Letchworth, UK.
Clarke, K.R. and R.M. Warwick. 1998. A taxonomic distinctness index and its statistical properties. J. Appl. Ecol. 35: 523–531.
Dalton, H. 1920. The measurement of the inequality of incomes. Econ. J. 30:348–361.
Faith, D.P. 1992. Conservation evaluation and phylogenic diversity. Biol. Conserv. 61: 1–10.
Faith, D.P 1995. Phylogenic pattern and the quantification of organismal biodiversity. In: D.L. Hawksworth (ed.), Biodiversity Measurement and Estimation. Chapman & Hall, London, pp. 45–58.
Gosselin, F. 2001. Lorenz partial order: the best known logical framework to define evenness indices. Community Ecol. 2: 197–207.
Hill, M.O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54: 427–431.
Izsák, J. and L. Papp. 1995. Application of the quadratic entropy index for diversity studies on drosophilid species assemblages. Environ. Ecol. Stat. 2: 213–224.
Izsák, J. and L. Papp. 2000. A link between ecological diversity indices and measures of biodiversity. Ecol. Model. 130: 151–156.
Magurran, A. 1988. Ecological Diversity and its Measurement. Princeton University Press, Princeton, NJ.
May, R.M. 1990. Taxonomy as destiny. Nature 347: 129–130.
Molinari, J. 1989. A calibrated index for the measurement of evenness. Oikos 56: 319–326.
Orlóci, L. 1991. Entropy and Information. SPB Academic Publishing, The Hague, NL.
Patil, G.P. and C. Taillie. 1979. An overview of diversity. In: J.F. Grassle, G.P. Patil, W. Smith and C. Taillie (eds.), Ecological Diversity in Theory and Practice. International Co-operative Publishing House, Fairland, MD, pp. 3–27.
Patil, G.P. and C. Taillie. 1982. Diversity as a concept and its measurement. J. Am. Stat. Ass. 77: 48–567.
Pielou, E.C. 1975. Ecological Diversity. Wiley Interscience, New York.
Rényi, A. 1961. On measures of entropy and information. In: G. Neyman (ed.), Proceedings of the fourth Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, California, Vol. 1, pp. 547–561.
Ricotta, C. 2002. Bridging the gap between ecological diversity indices and measures of biodiversity with Shannon’s entropy: comment to Izsák & Papp. Ecol. Model., in press.
Ricotta, C. and G.C. Avena. 2002. On the information-theoretical meaning of Hill’s parametric evenness. Acta Biotheoretica 50: 63–71.
Ricotta, C., A. Stanisci, G.C. Avena and C. Blasi. 2000. Quantifying the network connectivity of landscape mosaics: a graph-theoretical approach. Community Ecol. 1: 89–94.
Rogers, S., K.R. Clarke and J.D. Reynolds. 1999. The taxonomic distinctness of coastal bottom-dwelling fish communities of the North-east Atlantic. J. Anim. Ecol. 68: 769–782.
Shannon, C. 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27: 379–423.
Shimatani, K. 2001. On the measurement of species diversity incorporating species differences. Oikos 93: 135–147.
Simpson, E.H. 1949. Measurement of diversity. Nature 163: 688.
Solomon, D.L. 1979. A comparative approach to species diversity. In: J.F. Grassle, G.P. Patil, W. Smith and C. Taillie (eds.), Ecological Diversity in Theory and Practice. International Co-operative Publishing House, Fairland, MD, pp. 29–35.
Solow, A.R. and S. Polasky. 1994. Measuring biological diversity. Environ. Ecol. Stat. 1: 95–107.
Solow, A., S. Polasky and J. Brodaus. 1993. On the measurement of biological diversity. J. Environ. Econ. Manage. 24: 60–68.
Taillie, C. 1979. Species equitability: a comparative approach. In: J.F. Grassle, G.P. Patil, W. Smith and C. Taillie (eds,). Ecological Diversity in Theory and Practice. International Co-operative Publishing House, Fairland, MD, pp. 51–62.
Tóthmérész, B. 1995. Comparison of different methods for diversity ordering. J. Veg. Sci. 6: 283–290.
Vane-Wright, R.I., C.J. Humphries and P.M. Williams. 1991. What to protect: systematics and the agony of choice. Biol. Conserv. 55: 235–254.
Warwick, R.M. and K.R. Clarke. 1995. New ‘biodiversity’ measures reveal a decrease in taxonomic distinctness with increasing stress. Mar. Ecol. Prog. Ser 129: 301–305.
Wiener, H. 1947. Structural determination of paraffin boiling point. J. Amer. Chem. Soc. 69: 17–20.
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Ricotta, C. Measuring taxonomic diversity with parametric information functions. COMMUNITY ECOLOGY 3, 95–99 (2002). https://doi.org/10.1556/ComEc.3.2002.1.11
- Diversity profiles
- Information theory
- Rényi’s generalized information
- Set monotonicity